Proposal 1: Model-Based Control Method for Discrete-Parts machining processes

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1 Proposal 1: Model-Based Control Method for Discrete-Parts machining processes Proposed Objective: The proposed objective is to apply and extend the techniques from continuousprocessing industries to create a Model-Based Control (MBC) method to optimize discrete-parts machining processes. The proposal also aims at incorporating multiple target objectives such as profit, quality and time into the objective function in order to develop an optimal control strategy. The aim is to incorporate the models of the machining system into the control schemes. This work is specifically applied to discrete parts manufacturing by explicitly representing process physics in the control of machining processes. It is also proposed to extend this idea of model-based manufacturing control to manufacturing systems. This is proposed to be achieved by communicating individual process information and product quality measurements throughout the manufacturing network. Scientific Method: Model-Based Control is used to achieve higher quality of control as it is based on the underlying physics of the process rather than reactionary means. Traditionally, PID controls are used in the manufacturing process control, and they are oblivious underlying physical model of the system. On the other hand, Model Based control (MBC) schemes have been developed for continuous-processing industries, which are used to develop optimal control strategies for a given objective function. The proposed work aims at developing MBC techniques for the optimization of discrete parts machining processes with multiple target objectives. This research is proposed to be carried out in two parts, 1) Identify the potential of the model-based control methods to improve machining control at the process level. 2) Identify and address barriers to applicability of model-based methods at the system level. The goal is to have a network of machining operations, where the operations optimize themselves based on the model input from the upstream processes and the final-product quality signals from the downstream processes. The multiple objectives such as cost, power, quality is incorporated into a cost function which is a quadratic function of the residual error of the prediction, large changes to the control inputs, and error of the inputs to previous setpoints. The objective function is then used to design the optimal control. The technique original developed in control and systems theory has found wide applications to multitude of systems, including manufacturing process models and quality control. Intellectual Merit: The optimal control method based on the knowledge of the model is already developed and applied for manufacturing systems. The proposed objective is to apply the techniques to discrete parts machining processes, which is not an novel contribution or an innovation on its own. The theory of optimization in discrete-time and discrete-statespace has also been developed and used for a variety of practical systems. There are not many significant challenges nor potential for innovation or novel contributions based on the proposed research activity. Broader Impact: The research plans on engaging students from the STEM program and introducing intelligent manufacturing research in middle school curricula.

2 Proposal 2: Hybrid Molecular Dynamic and Monte Carlo Simulation of Nanometric Cutting Proposed Objective: The proposal aims at studying 1) The machining process by a hybrid Molecular Dynamic (MD) and Monte Carlo (MC) approach, in order to increase the effectiveness of nanometric cutting. The Monte Carlo approach is a statistical simulation tool that simulates only the key equilibrium properties of the underlying dynamics, thus saving computational time. This allows for simulation of machining process at the atomistic level and enables to study the effects of various factors such as the cutting speeds, cut depth, rake angle, edge radius etc. 2) Extend current simulation capabilities from modeling FCC metals to BCC and HCP metals using the Modified Embedded Atom Method(MEAM). 3) Increase processing speed by developing parallel processing schemes. 4) Reexamine the current cutting process by reducing the process size, identify new applications and potential limitations of the hybrid MD/MC method. Scientific Method: Conventional Molecular Dynamics (MD) simulations produce much more information than necessary to obtain equilibrium properties with a large computational overhead. It is for this reason that Monte Carlo (MC) methods are used to identify equilibrium properties. In this method, the particles are moved randomly and resultant configuration is either accepted or rejected based on a criterion. This step is iterated until the positions converge to equilibrium positions. However, due to the random nature of the movements, the convergence could take a large number of steps. The authors propose the use of MD simulation (damped trajectory and steepest gradient descent) steps to speed up the convergence of the MC iterations. The authors also propose a strategy based on isotherms to analyze the properties at conventional cutting speeds (which give rise to temperature gradients within the material). Secondly, the importance and use of many body interaction potential in studying the machining process is presented where it produces accurate results in case of nanometric cutting of silicon compared to pairwise potential for BCC and HCP structures. The proposal also aims at incorporating such many body potentials into MC simulations. Lastly, the proposal aims at implementing parallelization techniques for the MC simulation. The parallelization is intended to be carried out on the Beowulf cluster with the help of Message Passing(MPI) programming paradigm. The goal of this part is to develop a distributed computing system that can handle nanometric cutting simulations of systems of upto a million atoms. Significance and Broader Impact: The project aims to involve various graduate and undergraduate students from underrepresented groups to take part in the research activities. In addition, topics on nanometric cutting is also planned to included in the course content offered at the university. The authors are also preparing a textbook on Molecular dynamics techniques in nanometric cutting and tribology. Finally, the impact of the project to the overall economy where industries specializing in manufacturing processes could benefit from the technology is discussed. The aim of the proposed work is to develop technology on par with those used overseas that have a greater manufacturing focus than the U.S. The knowledge obtained via the research is then intended to be transferred to the industry.

3 Proposal 3: Joint Market and Supply Chain decisions for dynamic product planning. Proposed Objective: The proposal aims to analyze the joint market and supply chain decisions by utilizing the developed mathematical models. The scenarios include the entire life of the particular product and competitive interactions. The proposed work aims at 1) Establishing discrete choice models, with multi logit product demand modeling. 2) Study product planning and pricing under time varying demands and competitions, 3)Analyze market competition and supply channels(local, immediate, reliable and expensive, vs, remote, longer-time scale, and less expensive), distribution channels(manufacturer wholesale vs retailers) during product planning. Scientific Method: 1)For product demand modeling with mixed logit(ml), the authors plan to study methods to establish discrete choice method for product demand modeling. This consists of two steps a) Estimation of model parameters, b) Estimation of product family demand. For estimating the parameters of the model the authors propose to use a maximum likelihood method, which fits a statistical model to data with maximum probability. The authors also plan to use the Dynamic Differential Evolution algorithm for ML estimation. 2) For Dynamic Product planning and pricing the authors use a simple formula that expresses the profit margin as a function of various implicit and explicit manufacturing costs, as well as the customer demand, which is a linear time-varying, product-attribute dependent function. The profit margin is then maximized as a function of various parameters. Furthermore, under new product and competition, the profit margin is influenced due to additional forces that change adaptively. This is modified appropriately via game theoretical models, which account for price and product attribute competition. The authors propose to use Nash equilibrium model and Stackelberg game model to study and model competitive interactions. 3)For Adaptive product planning and pricing, the authors plan to develop an integrated computational model to support cross-functional decision making regarding product line mix. Intellectual Merit: The authors claim, fundamental and practical research on joint market and supply chain decisions. The research will utilize game theoretic models to analyze competition and new product planning. Optimal solutions, tools and mathematical models are also proposed to be developed. However, the proposed work on joint product placement and competition analysis seems very ad-hoc. The necessary tools, models and techniques for supply chain management analysis have been exensively studied and developed. The proposed project does not seem to employ or develop novel techniques in a field such as product planning or supply chain management. Broader Impact: The project aims at continuous dialog, feedback and technology transfer with the companies that supply case study material. The research work is also aimed at attracting students from all levels, from high school to grad school to participate and contribute to the research. Underrepresented groups will be involved and students will be encouraged to participate in NSF sponsored workshops.

4 Proposal 4: Portfolio Management and Energy Investment Proposed Objective: The proposal aims at applying Finite Difference Method to the problem of portfolio maximization, in the presence of proportional and fixed transaction costs. The proposal also aims to investigate the investment strategy and in a Green Power plant under the time-varying cost of electricity, cost and time of construction of the new plant etc. Scientific Method: This proposal aims to apply techniques from Finite Element Methods (FEM) specifically the Discontinuous Gelarkin (DG) Method, which is used for numerical solution to partial differential equations(pdes). The advantage of the method is the nature of the solution, which avoids spurious oscillations which can sometimes manifest in other types of numerical methods. Furthermore, the numerical method is also parallelizable for different computational platforms. The underlying equation for portfolio maximization is related to the diffusion equation in conventional fluid mechanics. Hence much of the techniques used for the solution of diffusion equations can be applied directly to the current problem in computational Finance. First the problem of portfolio maximization is converted to buy and hold problem which satisfies the linear complimentarity conditions. Next, the resulting PDE is transformed into a problem within a finite domain which is readily amenable to the DG method. The proposal also aims to apply this method of solution to the Options Pricing problem. The portfolio management problem with entry decisions is also proposed to be studied, where a case study of Energy Investment is considered. The cost of building a greener power plant is influenced by various factors, such as, cost of electricity, production rate of proposed power plant compared to rate of existing power plants, planning horizons, discount rate etc. This problem is again modeled as a stochastic optimization problem where techniques from stochastic control can be used to determine the optimal control and hence an optimal cost trajectory. Thus the proposal also aims at determining the optimal time line and Free Boundary for the problem. The mathematical equations and symbols used to describe the concepts are ambiguous. Intellectual Merit: The application of numerical solutions of PDEs to problems in financial engineering, which are modeled as diffusion equations and Hamilton Jacobi Bellman (HJB) Equations, has been studied extensively. This proposal aims at applying the DG method to compute the numerical solutions which yields absolutely convergent solutions with no spurious oscillations. Furthermore, the application of stochastic and optimal control solutions to financial engineering has also been studied. The proposed problem of Entry Decisions of Energy Investments is being studied with the above techniques, which might help financial engineers planning energy projects. Significance and Impacts: The proposal seeks to help investors, financial engineers and those seeking to maximize the value of their portfolio. The developed software suite is also planned to be made available for investors. There is also importance given to training and education apart from research activities. Several courses offered in financial engineering are planned to include the topics of the research. In

5 addition a graduate student pursuing doctoral degree will also be involved in the ongoing research activities. Proposal 5: GOALI Advanced Machining Processes for Lightweight Cast Metals Proposal Objective: The proposal aims to test the hypothesis that heating the work material at the point of machining will improve machinability and resulting microstructure. The technique is planned to be tested on brittle, cast metals, such as cast aluminum and magnesium alloys. The mechanical and subsurface properties are proposed to be characterized and measured. Finite element method is proposed to be used to model the machining of heated material with temperature dependent material properties. This research also proposes to investigate the effects of non-traditional machining and friction stir processes on the materials. Research Tasks: The research is planned to be carried out as the following tasks: 1) Characterize casting defects and temperature dependent material properties. This is achieved by independently measuring the effect of casting defects and temperature dependent effects with the help of controlled experiments. 2) Experimental investigation of nontraditional manufacturing process. This is achieved by first setting up stable, in-situ, high temperature machining experiments and monitoring various mechanical properties closely. This is followed by investigation of nontraditional cutting of cast metals, such as water jet and laser cutting. These methods potentially reduce the force and damage to the work material. The measurement of effects of the machining process on the microstructure is helpful to quantify the defects. 3) Finally a Finite element based computational modeling is proposed to be performed in order to simulate the effects of the machining techniques for current and future research. Broader Impact: The proposed research and collaboration activity plans to assist with the K-12 STEM outreach program, mentor undergraduate and underrepresented groups, encourage student participation at meetings and seminars and establish education collaboration with other faculty, students and staff from several neighboring underrepresented geographical areas. Proposal 6: A Concurrent Multi-resolution Framework for Deformation and Failure Analysis of Heterogeneous Materials Proposal Objective: The proposal aims at studying and quantifying structure-property relationships that regulate the deformation and failure behavior of advanced materials. The quantification of the effect of the evolution of microstructure and defect is proposed to be modeled via a finite element based multiresolution network. Two examples materials systems 1) nacre shells and build metallic glasses, both with micro-structural features that impact the macro-structural properties will be studied. Scientific Method: The proposal plan to use multi-scale algorithms that will concurrently resolve the physics of deformation and failure, and predict the macroscale mechanical behavior. The following salient methods are proposed to be used 1) Discrete Galerkin Finite Element based computational scheme that can handle discontinuities in the displacement field. This technique has the advantage of handling irregularities and discontinuities in the structure. 2) Simulation of faults in a mesh independent manner that enables the analysis of the evolution of faults in the structure across multiple length and

6 time scales. 3) High dimensional Model Representation based surrogate modeling in order to reduce the computational burden. Broader Impact: The research program will give students skills in computational materials development, involve graduate, undergraduate, and students from high schools in order to encourage enrollment in STEM. In addition the research knowledge is planned to be integrated in courses offered. The K12 outreach program, and virtual reality games based on mechanics is planned to make the research experience both productive and rewarding.